IE 111 Fall Semester 2009
Homework #3 Solutions
1) Samples of skin experiencing desquamation are analyzed for both moisture and
melanin content. The results from 100 skin samples are as follows:
Melanin
content
High
low
Moisture
high
13
7
Content
low
48
32
Let A denote the event that a sample has low melanin content, and let B denote the
event that sample has high moisture content. Determine the following probabilities:
a)
P(A)=(7+32)/100=0.39
b)
P(B)=(13+7)/100=0.2
c)
P(AB)=7/20=0.35
d)
P(BA)=7/39=0.179
2)
An integer is selected at random from {1, 2, …, 100}. Given that the number
selected is divisible by 2, find the probability that it is divisible by 3 or 5.
Solution: Let A_2 = event that the number is divisible by 2
Let A_3 = event that the number is divisible by 3
Let A_5 = event that the number is divisible by 5
P(A_3
∪
A_5 A_2) = P[(A_3
∪
A_5)
∩
A_2 ] / P(A_2)
= P [(A_3
∩
A_2)
∪
(A_5
∩
A_2) ] / P(A_2)
= P(A_3
∩
A_2) + P (A_5
∩
A_2)–P(A_3
∩
A_5
∩
A_2)/ P(A_2)
P(A_3
∩
A_2)
= 16/100, P (A_5
∩
A_2) = 10/100, P(A_3
∩
A_5
∩
A_2)= 3/100
P(A_3
∪
A_5  A_2)= (16/100 + 10/100 + 3/100) / (50/100) = 23/50 = 0.46
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
3) We have two coins, the first is fair and the second twoheaded. We pick one of the
coins at random, we toss it twice and heads shows both times. Find the probability that
the coin picked is fair.
Solution:
In this experiment, each outcome consists of a particular coin selection and two coin
tosses. So for example, fhh represents picking the fair coin and obtaining hh.
Now, the event
F ={the selected coin is fair}={fhh,fht, fth,ftt},
F
c
= {the selected coin is twoheaded}={f
c
hh}
P(F)=P(F
c
) =1/2
P(hhF)=1/4,
p(hhF
c
)=1
We want to find P (Fhh), so
P(hh)= P(hhF)P(F) +
P(hhF
c
)P(F
c
) =5/8
P(F/hh)= P(hh/F)P(F)/ P(hh) = (1/4) (1/2) / (5/8) =1/5
4) A lot of 50 semiconductors chips contains 10 that are defective. Two chips are selected
at random, without replacement, from the lot.
a) What is the probability that the first one selected is defective?
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '07
 Storer
 Probability theory, Cumulative distribution function, Probability mass function

Click to edit the document details